AND ON THE DIURNAL INEQUALITY. 
7 
no longer common, such as confounding the time of high water with the time of 
turn of the tide-stream. But there is probably still some unnecessary difficulty pro- 
duced by regarding, as a cardinal point in the observation, the “ establishment,” as 
vulgarly understood, namely the hour of high water on the day of new or full moon ; 
for, in fact, the hour of high water on this day is of no more importance than the 
hour of high water on any other day, except in so far as it gives the means of know- 
ing the hour on other days. And it does not afford the means of doing this, any 
more than the hour of high-water for any other given age of the moon does. For 
just as much inaccuracy as, from whatever cause, there is, in deducing the time of 
high water at all ages of the moon from the time at a given age, just so much inac- 
curacy is there, from the same causes, in deducing the time of high water for all 
ages of the moon, from the time for full or new moon. And if the time at which the 
tide follows the moon on two or three successive occasions, be greatly and irregularly 
different, the observations are equally of little value, (either for drawing cotidal lines, 
or for predicting tides, or for any other purpose,) whether any of the observed tides 
fall on the day of new or full moon, or do not. If the tides are regular and the ob- 
servations good, the common “ establishment” may be obtained from the observa- 
tions of any one day ; although to give much value to this deduction, the tides should 
be observed for a fortnight. And if such observations be made for a number of very 
distant places, the common “establishment” does not represent a corresponding fact 
at different places. In some places it means the time of high water one day after 
the highest tide ; in some, the time two days after the highest tide ; in some, three 
days ; for the “ age of the tide” is different at different places, and the tide which 
corresponds to the new or full moon comes after the new or full moon by one, two, 
or three days. Hence, in order that we might compare the tides of distant places 
by means of a fact which had the same meaning in all of them, I proposed, in my 
former Essay, instead of taking this common Establishment, to take what I then 
called the corrected Establishment, namely the mean of all the lunitidal intervals, that 
is, of the intervals by which the tide follows the moon’s transit. And this corrected 
establishment I used in the discussion of the extensive series of observations made in 
1836. In general, the corrected establishment is about thirty minutes less than the 
common establishment. It has been used by Admiral Lutke in his discussion of the 
tides of the Pacific. As however the common establishment is still the one familiar 
to navigators, and as no material error will result from the use of it, I shall make it 
the basis of my remarks on the tides of the Pacific. But it may be useful to bear 
in mind what I have said, that this “ establishment” may be deduced from observa- 
tions not made at the new or full moon*. 
A very simple and convenient way of recording the result of a tide observation on 
any day, would be to state the time of moons transit (which is given by the tables 
* I have here said that in cases where the tides follow the common laws, we may deduce the time of high 
water on one day from the time on another : I might have said the same thing of the heights. 
